We investigate a reformulation of Yang-Mills theory at the level of the expectation of the non-abelian Wilson loop using a string theory with non-standard interaction. We find that the path-ordering of the Wilson loop can be generated either from considering a worldsheet generalisation of a boundary theory or by introducing a gauge field onto the worldsheet. Only the gauge theory has the sufficient structure to accommodate the three gluon vertex of Yang-Mills theory in the string model. Supersymmetric analogues of these two models are also investigated which, specifically in the gauge theory model, can be made the basis of a realistic string model formulation of Yang-Mills theory coupled to spinors
